Lifetime energy potential

The measurement of fluorescence lifetimes is an integral part of the anisotropy, energy transfer, and quenching experiment. Also, the fluorescence lifetime provides potentially useful information on the fluorophore environment and therefore provides useful information on membrane properties. An example is the investigation of lateral phase separations. Recently, interest in the fluorescence lifetime itself has increased due to the introduction of the lifetime distribution model as an alternative to the discrete multiexponential approach which has been prevalent in the past. 

Light absorption leading to electronic excitation is commonly accompanied by radiative reemission as the electron decays back to the ground potential energy surface. However, in certain cases (dependent on excited-state radiative lifetime and potential features to be described below) the system returns to the ground electronic surface without optical emission, a so-called radiationless transition. Such non-radiative transition processes are important features of reaction pathways on both ground and excited surfaces. 

It is the relationship between the bound potential energy surface of an adsorbate and the vibrational states of the molecule that detemiine whether an adsorbate remains on the surface, or whether it desorbs after a period of time. The lifetime of the adsorbed state, r, depends on the size of the well relative to the vibrational energy inlierent in the system, and can be written as... 

In a time-dependent picture, resonances can be viewed as localized wavepackets composed of a superposition of continuum wavefimctions, which qualitatively resemble bound states for a period of time. The unimolecular reactant in a resonance state moves within the potential energy well for a considerable period of time, leaving it only when a fairly long time interval r has elapsed r may be called the lifetime of the almost stationary resonance state. 

Such diagrams make clear the difference between an intermediate and a transition state. An intermediate lies in a depression on the potential energy curve. Thus, it will have a finite lifetime. The actual lifetime will depend on the depth of the depression. A shallow depression implies a low activation energy for the subsequent step, and therefore a short lifetime. The deeper the depression, the longer is the lifetime of the intermediate. The situation at a transition state is quite different. It has only fleeting existence and represents an energy maximum on the reaction path. 

Fig. 20. Bond scission activation energy and lifetime (Tt) plotted as a function of applied force. The solid curve is derived from Eq. (65) based on the Morse potential, the other data are redrawn from Ref. [101]. The upper abscissa gives the overall elastic strain before failure. The numbers indicate the minimum chain lengths which will fail at a particular force...

A careful distinction must be drawn between transition states and intermediates. As noted in Chapter 4, an intermediate occupies a potential energy minimum along the reaction coordinate. Additional activation, whether by an intramolecular process (distortion, rearrangement, dissociation) or by a bimolecular reaction with another component, is needed to enable the intermediate to react further it may then return to the starting materials or advance to product. One can divert an intermediate from its normal course by the addition of another reagent. This substance, referred to as a trap or scavenger, can be added prior to the start of the reaction or (if the lifetime allows) once the first-formed intermediate has built up. Such experiments are the trapping experiments referred to in Chapters 4 and 5. 

The PMC transient-potential diagrams and the equations derived for PMC transients clearly show that bending of an energy band significantly influences the charge carrier lifetime in semiconductor/electrolyte junctions and that an accurate interpretation of the kinetic meaning of such transients is only possible when the band bending is known and controlled. 

---